To determine the relative frequencies for the given survey data, we need to follow these steps:
### 1. Relative Frequency for Students Who Have Been to Alaska
- Total number of students surveyed: [tex]\( 50 \)[/tex]
- Number of students who have been to Alaska: [tex]\( 14 \)[/tex]
The relative frequency, [tex]\( f \)[/tex], for students who have been to Alaska is calculated as:
[tex]\[ f = \frac{\text{Number of students who have been to Alaska}}{\text{Total number of students surveyed}} \][/tex]
[tex]\[ f = \frac{14}{50} \][/tex]
[tex]\[ f = 0.28 \][/tex]
So, the relative frequency for students who have been to Alaska is [tex]\( \boxed{0.28} \)[/tex].
### 2. Relative Frequency for Students Who Have Been to Hawaii but Not Alaska
- Total number of students surveyed: [tex]\( 50 \)[/tex]
- Number of students who have been to Hawaii but not Alaska: [tex]\( 15 \)[/tex]
The relative frequency, [tex]\( f \)[/tex], for students who have been to Hawaii but not Alaska is calculated as:
[tex]\[ f = \frac{\text{Number of students who have been to Hawaii but not Alaska}}{\text{Total number of students surveyed}} \][/tex]
[tex]\[ f = \frac{15}{50} \][/tex]
[tex]\[ f = 0.3 \][/tex]
So, the relative frequency for students who have been to Hawaii but not Alaska is [tex]\( \boxed{0.3} \)[/tex].
### 3. Relative Frequency for Students Who Have Not Been to Alaska or Hawaii
- Total number of students surveyed: [tex]\( 50 \)[/tex]
- Number of students who have not been to Alaska or Hawaii: [tex]\( 21 \)[/tex]
The relative frequency, [tex]\( f \)[/tex], for students who have not been to Alaska or Hawaii is calculated as:
[tex]\[ f = \frac{\text{Number of students who have not been to Alaska or Hawaii}}{\text{Total number of students surveyed}} \][/tex]
[tex]\[ f = \frac{21}{50} \][/tex]
[tex]\[ f = 0.42 \][/tex]
So, the relative frequency for students who have not been to Alaska or Hawaii is [tex]\( \boxed{0.42} \)[/tex].
In summary:
- The relative frequency for students who have been to Alaska is [tex]\( 0.28 \)[/tex].
- The relative frequency for students who have been to Hawaii but not Alaska is [tex]\( 0.3 \)[/tex].
- The relative frequency for students who have not been to Alaska or Hawaii is [tex]\( 0.42 \)[/tex].
